Science for the School and Family, Part I. Natural Philosophy

by Worthington Hooker

197. Friction of Liquids in Tubes.—So easily does water flow along that we should not at first view suppose that it would be delayed much from friction as it passes through pipes or along channels. But the retarding influence is considerable. An inch tube 200 feet long, lying horizontally connected with a reservoir, will discharge water not one quarter as fast as an inch orifice in the side of the reservoir. Sudden turns in a pipe should be avoided, because they occasion so much friction against the sides of the pipe and among the particles of water by disturbing the regularity of the current. In the entrance of the arteries into the brain, in order to prevent the blood from flowing too rapidly into this organ, there are sudden turns in the arteries to retard the blood; and in grazing animals, as there is special danger that the blood will flow too freely to the brain as the head is held down in eating, there is a special provision to prevent this in a net-work of arteries. If the arteries of the brain in such animals were straight tubes they would continually be dying of congestion of the brain or of apoplexy.

Fig. 131.

Friction in a small pipe is greater in proportion to its size than in a large pipe. In a pipe an inch in diameter water will not move more than one-fifth as fast as in a tube two inches in diameter. This may be made clear by Fig. 131, in which is represented the area of a small tube inside of the area of a tube of twice its diameter. Suppose the effect of the friction in the large tube to extend in to a. In the small one it will extend in as far, that is, to b. But e a is about five times as long as e b, so that there is full five times as much water clear of friction in the large tube as there is in the smaller one.

Fig. 132.

198. Friction in Streams.—The retarding effect of friction is very obvious in brooks and rivers. The water in the middle of a stream runs much more rapidly than it does near its banks. When a river is very shallow at its sides the water there scarcely moves, though in the middle the water may be running at a rapid rate. A tide, therefore, flowing up a river, moves more freely near its banks than it does in the middle of the stream, because it meets with less resistance there from the downward current. Water moves less rapidly at the bottom of a river than it does at the surface. For this reason, if a stick be so loaded at one end as to stand upright in water, in the current of a river its upper end will be carried along faster than its lower end, and therefore it will incline forward, as in Fig. 132. As the sea rolls in over a beach, each wave at length pours over its crest and breaks, because the lower part of the wave is retarded by friction on the beach. Were it not for the constant retardation of friction at the sides and bottom of rivers, and at their bends, those rivers which have their rise at a considerable height above the level of the sea would acquire an immense velocity. Thus the Rhone, drawing its waters from 1000 feet above the level of the ocean, would pour them forth with the velocity of water which had fallen perpendicularly the same height, that is, at the rate of 170 miles an hour, did not friction continually diminish the velocity.

199. Waves.—Waves are generally formed by the friction of air upon water. Observe how they are formed. As soon as any portion of water is raised above the general surface it tends by gravity to fall to a level with the water around it, and in doing so the portion next to it is forced upward, forming another wave; and so one wave produces another, each one being smaller than the preceding, till at length the motion is wholly lost. This is always the process when the cause of the motion is a single impulse, as when a stone is dropped into the water. But when the waves are produced by a succession of impulses, as when wind makes them, they are mostly of the same size. It is quite a common notion that the water moves as rapidly as the waves appear to do; but the water really remains nearly stationary, rising and falling, while merely the form of the wave advances. The same wave is made up continually of a succession of different portions of water, or rather it is a succession of different waves. This is very well illustrated by the waving of a rope or carpet. In an open sea a wave slopes regularly on either side; but when it comes near the shore, for the reason given in § 198, it grows more and more nearly perpendicular on the side toward the shore, till at length it falls over, and if it be very large the roar thus caused by its breaking is heard to a great distance.

200. Height of Waves.—"So awful," says Dr. Arnot, "is the spectacle of a storm at sea that it is generally viewed through a medium which biases the judgment; and lofty as waves really are, imagination pictures them loftier still. Now no wave rises more than ten feet above the ordinary sea-level, which, with the ten feet that its surface afterward descends below this, gives twenty feet for the whole height from the bottom of any water-valley to an adjoining summit. This proposition is easily verified by a person who tries at what height on a ship's mast the horizon remains always in sight over the top of the waves—allowance being made for accidental inclinations of the vessel, and for her sinking in the water to much below her water-line, at the time when she reaches the bottom of the hollow between two waves. The spray of the sea, driven along by the violence of the wind, is of course much higher than the summit of the liquid wave; and a wave, coming against an obstacle, may dash to a great elevation above it. At the Eddystone Light-house, when a surge breaks which has been growing under a storm all the way across the Atlantic, it dashes even over the lantern at the summit."

201. Momentum.—The momentum of a body is its force when in motion. In estimating the momentum of any body two things must be considered—its velocity, and its quantity of matter or weight. A bullet fired from a gun has a vastly greater force, or power of overcoming obstacles, than one thrown by the hand, from its greater velocity. Now suppose the weight or quantity of matter to be increased ten times, and that it moves with the same velocity as before, it will have ten times as much force as before, and will overcome ten times as great an obstacle. For this reason a small stone dropping upon a man's head may do but little harm, while one ten times as large, falling from the same height, may stun and perhaps kill him. But if the large stone could fall with only one-tenth of the velocity of the small one, the effect of both would be the same. Let this example illustrate the rule for calculating the momentum of moving bodies, viz., multiply the quantity of matter into the velocity: Let the weight of the small stone be 1 ounce, and that of the large one 10 ounces. If they fall from a height of 16 feet the force with which the large one will strike will be expressed by 160 (16×10), that of the small one by 16 (1×16). Suppose, now, that by some force in addition to gravity the small one could be made to move ten times as fast as the large one, the force with which it would strike would be equal to that of the large one, and would be expressed by the number 160.